Understanding circadian clock mechanisms is fundamental in order to counteract the harmful effects of clock malfunctioning and associated diseases. Biochemical, genetic and systems biology approaches have provided invaluable information on the mechanisms of the circadian clock, from which many mathematical models have been developed to understand the dynamics and quantitative properties of the circadian oscillator. To better analyze and compare quantitatively all these circadian cycles, we propose a method based on a previously proposed circadian cycle segmentation into stages. We notably identify a sequence of eight stages that characterize the progress of the circadian cycle. Next, we apply our approach to an experimental dataset and to five different models, all built with ordinary differential equations. Our method permits to assess the agreement of mathematical model cycles with biological properties or to detect some inconsistencies. As another application of our method, we provide insights on how this segmentation into stages can help to analyze the effect of a clock gene loss of function on the dynamic of a genetic oscillator. The strength of our method is to provide a benchmark for characterization, comparison and improvement of new mathematical models of circadian oscillators in a wide variety of model systems.